Download Nick-Watkins-EGU 2013

Geophysical Research Abstracts
Vol. 15, EGU2013-13733-1, 2013
EGU General Assembly 2013
© Author(s) 2013. CC Attribution 3.0 License.
The scaling of wild events in stochastic models: The Fisher limit, the
Mandelbrot limit, and FARIMA as a model of the intermediate cases
Nicholas Watkins (1,2,3)
(1) British Antarctic Survey, Cambridge, CB3 0ET, UK, (2) Centre for the Analysis of Time Series, LSE, Houghton Street,
London, UK, (3) University of Warwick, Coventry, CV4 7AL, UK
Stochastic modelling is of increasing importance, both specifically in climate science and more broadly across
the whole of nonlinear geophysics. Traditionally, the noise components of such models would be spectrally white
(delta-correlated) and Gaussian in amplitude, and their variance (first named by Fisher in 1918) would well
characterise the likely size of fluctuations. Integration, for example in autoregressive models like AR(1), would
redden a noise spectrum, while multiplication in turbulent cascades could greatly increase the range of fluctuation
amplitudes, but such processes would still inherit aspects of their finite variance building blocks.
In the 60s and 70s, however, Mandelbrot and others [see e.g. Watkins, GRL Frontiers, 2013] began to
present evidence in nature for much stronger departures from Gaussianity (via very heavy tailed, infinite variance,
distributions) and from white noise (through long range dependence (LRD) in time). He also observed intermittency, defined here as correlations between absolute magnitudes in some time series, in, for example, finance and
turbulence. He proposed various models, including self-similar ones for heavy tails and LRD, and multifractal
cascades for intermittency.
In this presentation we compare contrasting types of model by looking at the "wild" events that they produce. The notion of a "wild" event can be made more precise in many ways, including by its duration in time, peak
amplitude, and spatial extent. Our chosen measure will be the "burst", defined as the area of a time series above a
fixed threshold. We will compare burst scaling in a self-similar, LRD, heavy tailed model (LFSM, e.g. Watkins et
al, PRE, 2009] with our newer results for multifractal random walks [with M. Rypdal and O. Lovsletten], and for
the heavy tailed extended version of the FARIMA (1,d,0) process, which combines long range dependence with
the high frequency structure familiar from AR(1). We will also discuss the physical meaning of FARIMA and its
potential as a modelling tool.
Geophysical Research Abstracts
Vol. 15, EGU2013-5738, 2013
EGU General Assembly 2013
© Author(s) 2013. CC Attribution 3.0 License.
Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes
Timothy Graves (1,4), Nicholas Watkins (2), Christian Franzke (2), and Robert Gramacy (3)
(1) University of Cambridge, Statistics Laboratory, Cambridge, United Kingdom. , (2) British Antarctic Survey, Cambridge,
United Kingdom ([email protected]) , (3) Booth School of Business, The University of Chicago, Chicago, IL, United
States. , (4) URS Corporation, 6-8 Greencoat Place, London, United Kingdom
Recent studies [e.g. the Antarctic study of Franzke, J. Climate, 2010] have strongly suggested that surface
temperatures exhibit long-range dependence (LRD). The presence of LRD would hamper the identification of
deterministic trends and the quantification of their significance. It is well established that LRD processes exhibit
stochastic trends over rather long periods of time. Thus, accurate methods for discriminating between physical
processes that possess long memory and those that do not are an important adjunct to climate modeling. As we
briefly review, the LRD idea originated at the same time as H-selfsimilarity, so it is often not realised that a model
does not have to be H-self similar to show LRD [e.g. Watkins, GRL Frontiers, 2013].
We have used Markov Chain Monte Carlo algorithms to perform a Bayesian analysis of Auto-Regressive
Fractionally-Integrated Moving-Average ARFIMA(p,d,q) processes, which are capable of modeling LRD. Our
principal aim is to obtain inference about the long memory parameter, d, with secondary interest in the scale and
location parameters. We have developed a reversible-jump method enabling us to integrate over different model
forms for the short memory component. We initially assume Gaussianity, and have tested the method on both
synthetic and physical time series.
Many physical processes, for example the Faraday Antarctic time series, are significantly non-Gaussian.
We have therefore extended this work by weakening the Gaussianity assumption, assuming an alpha-stable
distribution for the innovations, and performing joint inference on d and alpha. Such a modified FARIMA(p,d,q)
process is a flexible, initial model for non-Gaussian processes with long memory. We will present a study of the
dependence of the posterior variance of the memory parameter d on the length of the time series considered. This
will be compared with equivalent error diagnostics for other measures of d.
Geophysical Research Abstracts
Vol. 15, EGU2013-5526, 2013
EGU General Assembly 2013
© Author(s) 2013. CC Attribution 3.0 License.
Compound Extremes and Bunched Black (or Grouped Grey) Swans.
Nicholas Watkins (1,2,3)
(1) British Antarctic Survey, Cambridge, United Kingdom ([email protected]), (2) Centre for the Analysis of Time Series, LSE,
London, UK, (3) Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK
Observed “wild” natural fluctuations may differ substantially in their character. Some events may be genuinely
unforeseen (and unforeseeable), as with Taleb’s “black swans”. These may occur singly, or may have their impact
further magnified by being “bunched” in time. Some of the others may, however, be the rare extreme events from a
light-tailed underlying distribution. Studying their occurrence may then be tractable with the methods of extreme
value theory [e.g. Coles, 2001], suitably adapted to allow correlation if that is observed to be present.
Yet others may belong to a third broad class, described in today’s presentation [ reviewed in Watkins, GRL
Frontiers, 2013, doi: 10.1002/grl.50103]. Such “bursty” time series may show comparatively frequent high
amplitude events, and/or long range correlations between successive values. The frequent large values due to the
first of these effects, modelled in economics by Mandelbrot in 1963 using heavy- tailed probability distributions,
can give rise to an “IPCC type I” burst composed of successive wild events. Conversely, long range dependence,
even in a light-tailed Gaussian model like Mandelbrot and van Ness’ fractional Brownian motion, can integrate
“mild” events into an extreme “IPCC type III” burst.
I will show how a standard statistical time series model, linear fractional stable motion (LFSM), which descends from the two special cases advocated by Mandelbrot, allows these two effects to be varied independently,
and will present results from a preliminary study of such bursts in LFSM. The consequences for burst scaling when
low frequency effects due to dissipation (FARIMA models), and multiplicative cascades (such as multifractals)
are included will also be discussed, and the physical assumptions and constraints associated with making a given
choice of model.
Geophysical Research Abstracts
Vol. 15, EGU2013-7386, 2013
EGU General Assembly 2013
© Author(s) 2013. CC Attribution 3.0 License.
A spatio-temporal analysis of US station temperature trends over the last
century
Vincenzo Capparelli (1), Christian Franzke (2), Antonio Vecchio (1), Mervyn P Freeman (2), Nicholas W.
Watkins (2,3,4), Vincenzo Carbone (1,5)
(1) Dipartimento di Fisica, Università della Calabria, Cosenza, Italy ([email protected]), (2) British Antarctic
Survey, Cambridge, UK, (3) Centre for the Analysis of Time Series, London School of Economics and Political Science,
Houghton Street, London, UK, (4) Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK, (5)
IPCF/CNR Università della Calabria, Cosenza, Italy
This study presents a nonlinear spatio-temporal analysis of 1167 station
temperature records from the United States Historical Climatology Network
covering the period from 1898 through 2008. We use the Empirical Mode
Decomposition (EMD) method to extract the generally nonlinear trends of each
station. The statistical significance of each trend is assessed against three
null models of the background climate variability, represented by stochastic
processes of increasing temporal correlation length. We find strong evidence that more
than 50 percent of all stations experienced a significant trend over the last
century with respect to all three null models. A spatio-temporal
analysis reveals a significant cooling trend in the South-East
and significant warming trends in the rest of the contiguous US.
It also shows that the warming trend appears to have migrated
equatorward and possibly also in altitude. This shows the complex
spatio-temporal evolution of climate change at local scales
Geophysical Research Abstracts
Vol. 15, EGU2013-4597-1, 2013
EGU General Assembly 2013
© Author(s) 2013. CC Attribution 3.0 License.
Mapping the changing pattern of local climate as an observed distribution
Sandra Chapman (1,4), David Stainforth (1,2), Nicholas Watkins (1,2,3)
(1) University of Warwick, Physics Dept., Coventry CV4 7AL, United Kingdom ([email protected], +44 2476
692016), (2) CATS, London School of Economics, London, United Kingdom, (3) British Antarctic Survey, Cambridge, United
Kingdom, (4) University of Tromso, Dept. of Mathematics and Statistics, Norway
It is at local scales that the impacts of climate change will be felt directly and at which adaptation planning
decisions must be made. This requires quantifying the geographical patterns in trends at specific quantiles in
distributions of variables such as daily temperature or precipitation. Here we focus on these local changes and on
the way observational data can be analysed to inform us about the pattern of local climate change. We present a
method[1] for analysing local climatic timeseries data to assess which quantiles of the local climatic distribution
show the greatest and most robust trends. We demonstrate this approach using E-OBS gridded data[2] timeseries
of local daily temperature from specific locations across Europe over the last 60 years. Our method extracts
the changing cumulative distribution function over time and uses a simple mathematical deconstruction of how
the difference between two observations from two different time periods can be assigned to the combination of
natural statistical variability and/or the consequences of secular climate change. This deconstruction facilitates
an assessment of the sensitivity of different quantiles of the distributions to changing climate. Geographical
location and temperature are treated as independent variables, we thus obtain as outputs the pattern of variation
in sensitivity with temperature (or occurrence likelihood), and with geographical location. We find as an output
many regionally consistent patterns of response of potential value in adaptation planning. We discuss methods to
quantify and map the robustness of these observed sensitivities and their statistical likelihood. This also quantifies
the level of detail needed from climate models if they are to be used as tools to assess climate change impact.
[1] S C Chapman, D A Stainforth, N W Watkins, 2013, On Estimating Local Long Term Climate Trends,
Phil. Trans. R. Soc. A, in press
[2] Haylock, M.R., N. Hofstra, A.M.G. Klein Tank, E.J. Klok, P.D.
Jones and M. New. 2008: A European daily high-resolution gridded dataset of surface temperature and precipitation. J. Geophys. Res (Atmospheres), 113, D20119, doi:10.1029/2008JD10201
Geophysical Research Abstracts
Vol. 15, EGU2013-4575-1, 2013
EGU General Assembly 2013
© Author(s) 2013. CC Attribution 3.0 License.
An observationally centred method to quantify local climate change as a
distribution
David Stainforth (1,2), Sandra Chapman (1,4), Nicholas Watkins (1,2,3)
(1) University of Warwick, Physics Dept., Coventry CV4 7AL, United Kingdom ([email protected], +44 2476
692016), (2) CATS, London School of Economics, London, United Kingdom, (3) British Antarctic Survey, Cambridge, United
Kingdom, (4) University of Tromso, Dept. of Mathematics and Statistics, Norway
For planning and adaptation, guidance on trends in local climate is needed at the specific thresholds relevant to
particular impact or policy endeavours. This requires quantifying trends at specific quantiles in distributions of
variables such as daily temperature or precipitation. These non-normal distributions vary both geographically and
in time. The trends in the relevant quantiles may not simply follow the trend in the distribution mean. We present
a method[1] for analysing local climatic timeseries data to assess which quantiles of the local climatic distribution
show the greatest and most robust trends. We demonstrate this approach using E-OBS gridded data[2] timeseries
of local daily temperature from specific locations across Europe over the last 60 years. Our method extracts
the changing cumulative distribution function over time and uses a simple mathematical deconstruction of how
the difference between two observations from two different time periods can be assigned to the combination of
natural statistical variability and/or the consequences of secular climate change. This deconstruction facilitates an
assessment of the sensitivity of different quantiles of the distributions to changing climate. Geographical location
and temperature are treated as independent variables, we thus obtain as outputs how the trend or sensitivity varies
with temperature (or occurrence likelihood), and with geographical location. These sensitivities are found to
be geographically varying across Europe; as one would expect given the different influences on local climate
between, say, Western Scotland and central Italy. We find as an output many regionally consistent patterns of
response of potential value in adaptation planning. We discuss methods to quantify the robustness of these
observed sensitivities and their statistical likelihood. This also quantifies the level of detail needed from climate
models if they are to be used as tools to assess climate change impact.
[1] S C Chapman, D A Stainforth, N W Watkins, 2013, On Estimating Local Long Term Climate Trends,
Phil. Trans. R. Soc. A, in press
[2] Haylock, M.R., N. Hofstra, A.M.G. Klein Tank, E.J. Klok, P.D. Jones and M. New. 2008: A European
daily high-resolution gridded dataset of surface temperature and precipitation. J. Geophys. Res (Atmospheres),
113, D20119, doi:10.1029/2008JD10201